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

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When dealing with motion in two-dimensions (two planes),
we add vectors along along an angle
Use the points of a compass to indicate direction
If the direction does not match one of the points exactly, we
measure the angle from the closest compass point and specify
which side of that direction your line is on
We become concerned with the idea of quadrants (that area between N,S,W,E)
Example 1:
If a plane is flying 10º east of north, what would the vector
diagram of look like?
This angle suggest that this vector is
pointing east and then turning 40º
towards north or [E 40º N]. The angle
can also suggest that this vector is also
pointing north and then turning 50º
towards east or [N 50º E]
Example 2
Measure the following angles taking into consideration the direction. Make sure that you use a
protractor to measure the angles. This reviews your knowledge of complementary angles!
This vector is 40° east of
the north line
[N 40°E]
[
]
[S 25°E]
[
]
[W 45°N]
[
(This is an alternate way of expressing the direction of the vector. It is
the same vector just looking at it in a different orientation)
**Important: It is convention to choose the angle that is less than 45° (N 40°E instead of E 50°N)
]
Example 3:
Write the size and direction of each of the following displacement vectors. Scale: 1cm = 10 km
Example 4:
Draw each of the following displacement and velocity vectors.
(A) 30 km [N40°E]
(B) 15 m/s [S15°W]
In this section, you will be determing resultant displacement vectors using Scale Diagrams
(with 2-Dimensions). Follow these guidelines by adding vectors using scale diagrams:
1. List the givens and unknown.
2. Calculate the length, to scale of each of the vectors.
3. Draw the compass symbol on your page with north pointing up.
4. Draw the first vector precisely using your ruler.
5. Draw your second vector with its tail at the head of the first.
6. Add as many vectors as necessary following this pattern.
7. Draw the resultant vector as an arrow from the tail of the first vector (initial) to the tail of the
second vector (final).
8. Use a protractor to find the resultant displacement vector’s angle for the nearest compass
point.
9. Measure the resultant displacement vector’s length with a ruler, and convert the length into an
actual size.
10. Write a statement using the size, units and direction of the resultant vector.
Example 5: Denise walks to Jen’s home by walking 400 m due east and 500 m due north. What is
Denise’s total displacement?
Scale:


The resultant displacement that you measure will probably be roughly
cm. If you
convert the using the scale we created, the actual resultant displacement is
m.
We can measure the angle by placing the protractor between the first vector and the resultant
vector. By doing so, we can determine that the angle for the resultant displacement is
.
Therefore the total displacement (
) is
.
Example 6: A cyclist travels 450 m [W 35° S] and then rounds a corner and travels 630 m
[W 60° N].
(A) What is the cyclist’s total displacement?
(B) If the whole motion takes 77 s, what is the cyclist’s average velocity?
HOMEWORK: Read Pages 60-64 and Complete Questions #1-3 and 5-9 on Page 65